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%I
%S 1,0,1,3,0,1,-2,9,0,1,5,-8,18,0,1,-4,25,-20,30,0,1,7,-24,75,-40,45,0,
%T 1,-6,49,-84,175,-70,63,0,1,9,-48,196,-224,350,-112,84,0,1,-8,81,-216,
%U 588,-504,630,-168,108,0,1,11,-80,405,-720,1470,-1008,1050,-240,135,0,1
%N A triangle of coefficients for polynomials: p(x,n)=(x + 1)^n - n*(x - 1)^(n - 1).
%C Row sums are:
%C {1, 1, 4, 8, 16, 32, 64, 128, 256, 512, 1024}.
%F p(x,n)=(x + 1)^n - n*(x - 1)^(n - 1); t(n,m)=coefficients(p(x,n)).
%e {1},
%e {0, 1},
%e {3, 0, 1},
%e {-2, 9, 0, 1},
%e {5, -8, 18, 0, 1},
%e {-4, 25, -20, 30, 0, 1},
%e {7, -24, 75, -40, 45, 0, 1},
%e {-6, 49, -84, 175, -70, 63, 0, 1},
%e {9, -48, 196, -224, 350, -112, 84, 0, 1},
%e {-8, 81, -216, 588, -504, 630, -168, 108, 0, 1},
%e {11, -80, 405, -720, 1470, -1008, 1050, -240, 135, 0, 1}
%t Clear[p, x, n]; p[x_, n_] = (x + 1)^n - n*(x - 1)^(n - 1); Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
%K uned,sign
%O 1,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008
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